package algorithm.problems.dynamic_programming;

/**
 * Created by gouthamvidyapradhan on 02/04/2017.
 * Given an unsorted array of integers, find the length of longest increasing subsequence.
 * <p>
 * For example,
 * Given [10, 9, 2, 5, 3, 7, 101, 18],
 * The longest increasing subsequence is [2, 3, 7, 101], therefore the length is 4. Note that there may be more than one LIS combination, it is only necessary for you to return the length.
 * <p>
 * Your algorithm should run in O(n2) complexity.
 * <p>
 * Follow up: Could you improve it to O(n log n) time complexity?
 */
public class LongestIncreasingSubsequence {
    /**
     * Main method
     *
     * @param args
     * @throws Exception
     */
    public static void main(String[] args) throws Exception {
        int[] nums = {9, 8, 7, 6};
        System.out.println(new LongestIncreasingSubsequence().lengthOfLIS(nums));
    }

    public int lengthOfLIS(int[] nums) {
        if (nums.length == 0) return 0;
        int[] A = new int[nums.length];
        int max = Integer.MIN_VALUE;
        for (int i = 0, l = nums.length; i < l; i++) {
            int lis = 1;
            for (int j = 0; j < i; j++) {
                if (nums[i] > nums[j])
                    lis = Math.max(lis, A[j] + 1);
            }
            A[i] = lis;
            max = Math.max(max, A[i]);
        }
        return max;
    }
}
